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Independent component analysis [[electronic resource] /] / Aapo Hyvärinen, Juha Karhunen, Erkki Oja
Independent component analysis [[electronic resource] /] / Aapo Hyvärinen, Juha Karhunen, Erkki Oja
Autore Hyvärinen Aapo
Pubbl/distr/stampa New York, : J. Wiley, c2001
Descrizione fisica 1 online resource (505 p.)
Disciplina 519.5
519.5/35
519.535
Altri autori (Persone) KarhunenJuha
OjaErkki
Collana Adaptive and learning systems for signal processing, communications, and control
Soggetto topico Multivariate analysis
Principal components analysis
ISBN 1-280-26480-2
9786610264803
0-470-30861-3
0-471-46419-8
0-471-22131-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; Preface; 1 Introduction; 1.1 Linear representation of multivariate data; 1.1.1 The general statistical setting; 1.1.2 Dimension reduction methods; 1.1.3 Independence as a guiding principle; 1.2 Blind source separation; 1.2.1 Observing mixtures of unknown signals; 1.2.2 Source separation based on independence; 1.3 Independent component analysis; 1.3.1 Definition; 1.3.2 Applications; 1.3.3 How to find the independent components; 1.4 History of ICA; Part I: MATHEMATICAL PRELIMINARIES; 2 Random Vectors and Independence; 2.1 Probability distributions and densities
2.2 Expectations and moments2.3 Uncorrelatedness and independence; 2.4 Conditional densities and Bayes' rule; 2.5 The multivariate gaussian density; 2.6 Density of a transformation; 2.7 Higher-order statistics; 2.8 Stochastic processes *; 2.9 Concluding remarks and references; Problems; 3 Gradients and Optimization Methods; 3.1 Vector and matrix gradients; 3.2 Learning rules for unconstrained optimization; 3.3 Learning rules for constrained optimization; 3.4 Concluding remarks and references; Problems; 4 Estimation Theory; 4.1 Basic concepts; 4.2 Properties of estimators
4.3 Method of moments4.4 Least-squares estimation; 4.5 Maximum likelihood method; 4.6 Bayesian estimation *; 4.7 Concluding remarks and references; Problems; 5 Information Theory; 5.1 Entropy; 5.2 Mutual information; 5.3 Maximum entropy; 5.4 Negentropy; 5.5 Approximation of entropy by cumulants; 5.6 Approximation of entropy by nonpolynomial functions; 5.7 Concluding remarks and references; Problems; Appendix proofs; 6 Principal Component Analysis and Whitening; 6.1 Principal components; 6.2 PCA by on-line learning; 6.3 Factor analysis; 6.4 Whitening; 6.5 Orthogonalization
6.6 Concluding remarks and referencesProblems; Part II: BASIC INDEPENDENT COMPONENT ANALYSIS; 7 What is Independent Component Analysis?; 7.1 Motivation; 7.2 Definition of independent component analysis; 7.3 Illustration of ICA; 7.4 ICA is stronger that whitening; 7.5 Why gaussian variables are forbidden; 7.6 Concluding remarks and references; Problems; 8 ICA by Maximization of Nongaussianity; 8.1 ""Nongaussian is independent""; 8.2 Measuring nongaussianity by kurtosis; 8.3 Measuring nongaussianity by negentropy; 8.4 Estimating several independent components; 8.5 ICA and projection pursuit
8.6 Concluding remarks and referencesProblems; Appendix proofs; 9 ICA by Maximum Likelihood Estimation; 9.1 The likelihood of the ICA model; 9.2 Algorithms for maximum likelihood estimation; 9.3 The infomax principle; 9.4 Examples; 9.5 Concluding remarks and references; Problems; Appendix proofs; 10 ICA by Minimization of Mutual Information; 10.1 Defining ICA by mutual information; 10.2 Mutual information and nongaussianity; 10.3 Mutual information and likelihood; 10.4 Algorithms for minimization of mutual information; 10.5 Examples; 10.6 Concluding remarks and references; Problems
11 ICA by Tensorial Methods
Record Nr. UNISA-996201887503316
Hyvärinen Aapo  
New York, : J. Wiley, c2001
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Independent component analysis [[electronic resource] /] / Aapo Hyvärinen, Juha Karhunen, Erkki Oja
Independent component analysis [[electronic resource] /] / Aapo Hyvärinen, Juha Karhunen, Erkki Oja
Autore Hyvärinen Aapo
Pubbl/distr/stampa New York, : J. Wiley, c2001
Descrizione fisica 1 online resource (505 p.)
Disciplina 519.5
519.5/35
519.535
Altri autori (Persone) KarhunenJuha
OjaErkki
Collana Adaptive and learning systems for signal processing, communications, and control
Soggetto topico Multivariate analysis
Principal components analysis
ISBN 1-280-26480-2
9786610264803
0-470-30861-3
0-471-46419-8
0-471-22131-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; Preface; 1 Introduction; 1.1 Linear representation of multivariate data; 1.1.1 The general statistical setting; 1.1.2 Dimension reduction methods; 1.1.3 Independence as a guiding principle; 1.2 Blind source separation; 1.2.1 Observing mixtures of unknown signals; 1.2.2 Source separation based on independence; 1.3 Independent component analysis; 1.3.1 Definition; 1.3.2 Applications; 1.3.3 How to find the independent components; 1.4 History of ICA; Part I: MATHEMATICAL PRELIMINARIES; 2 Random Vectors and Independence; 2.1 Probability distributions and densities
2.2 Expectations and moments2.3 Uncorrelatedness and independence; 2.4 Conditional densities and Bayes' rule; 2.5 The multivariate gaussian density; 2.6 Density of a transformation; 2.7 Higher-order statistics; 2.8 Stochastic processes *; 2.9 Concluding remarks and references; Problems; 3 Gradients and Optimization Methods; 3.1 Vector and matrix gradients; 3.2 Learning rules for unconstrained optimization; 3.3 Learning rules for constrained optimization; 3.4 Concluding remarks and references; Problems; 4 Estimation Theory; 4.1 Basic concepts; 4.2 Properties of estimators
4.3 Method of moments4.4 Least-squares estimation; 4.5 Maximum likelihood method; 4.6 Bayesian estimation *; 4.7 Concluding remarks and references; Problems; 5 Information Theory; 5.1 Entropy; 5.2 Mutual information; 5.3 Maximum entropy; 5.4 Negentropy; 5.5 Approximation of entropy by cumulants; 5.6 Approximation of entropy by nonpolynomial functions; 5.7 Concluding remarks and references; Problems; Appendix proofs; 6 Principal Component Analysis and Whitening; 6.1 Principal components; 6.2 PCA by on-line learning; 6.3 Factor analysis; 6.4 Whitening; 6.5 Orthogonalization
6.6 Concluding remarks and referencesProblems; Part II: BASIC INDEPENDENT COMPONENT ANALYSIS; 7 What is Independent Component Analysis?; 7.1 Motivation; 7.2 Definition of independent component analysis; 7.3 Illustration of ICA; 7.4 ICA is stronger that whitening; 7.5 Why gaussian variables are forbidden; 7.6 Concluding remarks and references; Problems; 8 ICA by Maximization of Nongaussianity; 8.1 ""Nongaussian is independent""; 8.2 Measuring nongaussianity by kurtosis; 8.3 Measuring nongaussianity by negentropy; 8.4 Estimating several independent components; 8.5 ICA and projection pursuit
8.6 Concluding remarks and referencesProblems; Appendix proofs; 9 ICA by Maximum Likelihood Estimation; 9.1 The likelihood of the ICA model; 9.2 Algorithms for maximum likelihood estimation; 9.3 The infomax principle; 9.4 Examples; 9.5 Concluding remarks and references; Problems; Appendix proofs; 10 ICA by Minimization of Mutual Information; 10.1 Defining ICA by mutual information; 10.2 Mutual information and nongaussianity; 10.3 Mutual information and likelihood; 10.4 Algorithms for minimization of mutual information; 10.5 Examples; 10.6 Concluding remarks and references; Problems
11 ICA by Tensorial Methods
Record Nr. UNINA-9910143176003321
Hyvärinen Aapo  
New York, : J. Wiley, c2001
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui